MathDB

We call a collection of weights (each weighing an integer value) basic if their total weight equals

500

and each object of integer weight not greater than

500

can be balanced exactly with a uniquely determined set of weights from the collection. (Uniquely means that we are not concerned with order or which weights of equal value are chosen to balance against a particular object, if in fact there is a choice.) (a) Find an example of a basic collection other than the collection of

500

weights each of value

1

. (b) How many different basic collections are there?
(D. Fomin, Leningrad)

Problem Statement